display all the ideas for this combination of texts
8 ideas
| 11211 | If a sound conclusion comes from two errors that cancel out, the path of the argument must matter [Rumfitt] |
| Full Idea: If a designated conclusion follows from the premisses, but the argument involves two howlers which cancel each other out, then the moral is that the path an argument takes from premisses to conclusion does matter to its logical evaluation. | |
| From: Ian Rumfitt ("Yes" and "No" [2000], II) | |
| A reaction: The drift of this is that our view of logic should be a little closer to the reasoning of ordinary language, and we should rely a little less on purely formal accounts. |
| 21611 | Formal semantics defines validity as truth preserved in every model [Williamson] |
| Full Idea: An aim of formal semantics is to define in mathematical terms a set of models such that an argument is valid if and only if it preserves truth in every model in the set, for that will provide us with a precise standard of validity. | |
| From: Timothy Williamson (Vagueness [1994], 5.3) |
| 21606 | 'Bivalence' is the meta-linguistic principle that 'A' in the object language is true or false [Williamson] |
| Full Idea: The meta-logical law of excluded middle is the meta-linguistic principle that any statement 'A' in the object language is either truth or false; it is now known as the principle of 'bivalence'. | |
| From: Timothy Williamson (Vagueness [1994], 5.2) | |
| A reaction: [He cites Henryk Mehlberg 1958] See also Idea 21605. Without this way of distinguishing bivalence from excluded middle, most discussions of them strikes me as shockingly lacking in clarity. Personally I would cut the normativity from this one. |
| 21605 | Excluded Middle is 'A or not A' in the object language [Williamson] |
| Full Idea: The logical law of excluded middle (now the standard one) is the schema 'A or not A' in the object-language. | |
| From: Timothy Williamson (Vagueness [1994], 5.2) | |
| A reaction: [He cites Henryk Mehlberg 1958] See Idea 21606. The only sensible way to keep Excluded Middle and Bivalence distinct. I would say: (meta-) only T and F are available, and (object) each proposition must have one of them. Are they both normative? |
| 11212 | The sense of a connective comes from primitively obvious rules of inference [Rumfitt] |
| Full Idea: A connective will possess the sense that it has by virtue of its competent users' finding certain rules of inference involving it to be primitively obvious. | |
| From: Ian Rumfitt ("Yes" and "No" [2000], III) | |
| A reaction: Rumfitt cites Peacocke as endorsing this view, which characterises the logical connectives by their rules of usage rather than by their pure semantic value. |
| 11210 | Standardly 'and' and 'but' are held to have the same sense by having the same truth table [Rumfitt] |
| Full Idea: If 'and' and 'but' really are alike in sense, in what might that likeness consist? Some philosophers of classical logic will reply that they share a sense by virtue of sharing a truth table. | |
| From: Ian Rumfitt ("Yes" and "No" [2000]) | |
| A reaction: This is the standard view which Rumfitt sets out to challenge. |
| 21612 | Or-elimination is 'Argument by Cases'; it shows how to derive C from 'A or B' [Williamson] |
| Full Idea: Argument by Cases (or or-elimination) is the standard way of using disjunctive premises. If one can argue from A and some premises to C, and from B and some premises to C, one can argue from 'A or B' and the combined premises to C. | |
| From: Timothy Williamson (Vagueness [1994], 5.3) |
| 21599 | A sorites stops when it collides with an opposite sorites [Williamson] |
| Full Idea: A sorites paradox is stopped when it collides with a sorites paradox going in the opposite direction. That account will not strike a logician as solving the sorites paradox. | |
| From: Timothy Williamson (Vagueness [1994], 3.3) |